You can't spend all your time answering questions. Completing other tasks on the site (and there's always things to be done) is another great way to contribute to the community and carry on learning. To name a couple of my personal favourites,
- Handling flags (>10K)
- Participating in meta
All of these things contribute to the community, help you learn more about the site, how it works, how to make it work for you and done right this can also teach others by example.
Since the live-refresh feature was introduced, the method you describe is probably the best way to track posts that interest you. Keep those tabs open and open new questions in a new tab leaving the original tab in place to receive more updates. If you have some down time and (depending on your time zone) the questions are not coming in so fast (or you are interested in a less popular tag), head on over to your review tools or go over your old answers improving/editing where you can to ensure all your posts are up to date.
Meta is a fantastic way to learn the inner workings of the systems here. Being aware of what's going on in Meta is also the best way to stay up to date on new features that are coming out or to give feedback on existing features. Getting to know the system will also help you make the most of your time when answering questions. Plus they have casual Friday on meta - gotta love those...
If anything, doing any one of the things I've listed should pass enough time for your browsers title bar to start looking like this -